Abstract: Improvements are obtained in key generation and cryptographic applications in public key cryptography, by reducing the bit-length of public keys, thereby reducing the bandwidth requirements of telecommunications devices, such as wireless telephone sets.

Abstract: Cyclotomic polynomials are used to construct subgroups of multiplicative groups of finite fields that allow very efficient implementation of discrete logarithm based public key cryptosystems, including public key encryption schemes and digital signature schemes. A field is represented with an optimal normal basis, and a generator of a subgroup of the multiplicative group of the field is used to form a public key.

Abstract: Techniques are provided for generation of an RSA modulus having a predetermined portion. The predetermined portion may be the leading digits of the modulus, or split between the leading and trailing digits of the modulus. The resulting RSA modulus has the same security level as conventional RSA moduli, but requires less storage space. Significant performance improvements may be obtained for encryption, decryption, digital signature generation and digital signature verification when using RSA moduli in a specifically chosen format, as the division portion of a modulo operation is accomplished using only multiplication operations, and without using division operations.

Abstract: Techniques are provided for generation of an RSA modulus having a predetermined portion. The predetermined portion may be the leading digits of the modulus, or split between the leading and trailing digits of the modulus. The resulting RSA modulus has the same security level as conventional RSA moduli, but requires less storage space. Significant performance improvements may be obtained for encryption, decryption, digital signature generation and digital signature verification when using RSA moduli in a specifically chosen format, as the division portion of a modulo operation is accomplished using only multiplication operations, and without using division operations.

Abstract: Participants in a cryptosystem select their own elliptic curve and finite field, rather than using a centrally chosen elliptic curve. The curve is chosen from a predetermined set of elliptic curves expressed as Weierstra&bgr; model equations. The public key is based on a participant's unique ID, which must be exchanged during communication setup for non-cryptographic reasons, and a randomly chosen bitstring having a length based on security considerations. The public key can be readily constructed from parameters and mapping functions which are known system-wide and from a small amount of participant dependent data.

Abstract: Techniques are provided for generation of an RSA modulus having a predetermined portion. The predetermined portion may be the leading digits of the modulus, or split between the leading and trailing digits of the modulus. The resulting RSA modulus has the same security level as conventional RSA moduli, but requires less storage space. Significant performance improvements may be obtained for encryption, decryption, digital signature generation and digital signature verification when using RSA moduli in a specifically chosen format, as the division portion of a modulo operation is accomplished using only multiplication operations, and without using division operations.

Abstract: A method, system, and computer program product initializes a cryptosystem that implements XTR by reformulating an irreducibility test of a polynomial of the form F(c,X)=X3−cX2+cpX−1&egr;GF(p2)[X], for random c&egr;GF(p2), as an irreducibility problem for a third-degree polynomial of the form P(c,X)=X3+(cp+c)X2+(cp+1+cp+c−3)X+c2p+c2+2−2cp−2c, and testing the third-degree polynomial for irreducibility over GF(p). Testing the third-degree polynomial comprises eliminating the coefficient of X2 from P(c,X) to generate the polynomial P(c,X−(cp+c)/3)=X3+ƒ1X+ƒ0, and computing a discriminant &Dgr;=ƒ02+4ƒ13/27&egr;GF(p) by considering a polynomial of the form X2+ƒ0X−(ƒ1/3)3.

Abstract: A key escrow technique is disclosed which permits cryptographic limits on wiretapping warrants. Specifically, time limits on wiretaps may be enforced. In addition, the wiretapper is targeted to a specific party or specific pairs of parties communicating in a network.